Question

A scientist wants to see if the type of four vitamin supplements (A, B, C, D) affects the weight gain (y in grams) of laboratory animals. The experiment was conducted in a completely randomized design with five separately caged animals for each treatment. Since the caloric intake (in calories/10) will differ among animals and influence y, she wants to take this variable into account in the analysis. The data are given in the following table: Supplement Supplement Supplement y 48 35 67 44 78 44 69 51 53 47 y 1 65 40 49 45 37 37 73 53 63 42 y 7951 52 41 63 47 65 47 67 48 Supplementy 59 53 50 52 5952 42 51 34 43 Let the significance level a = 0.05. For each of the following questions, include the necessary out- put/plots/numbers to answer the questions and give a complete commentary on the results, written in report style:

This problem is using R.

Can an expert answer this question? I also need to find the anova and its summary from R.

Answer 1

The code is given for both anova and ancova in R

Note: I have put the data in csv and simply imported it in R. data_df <- read.csv ("data.csv", stringsAsFactors = F, header - T) head (data_df, 20) 1 ## ## ## ## Supplement y X A 48 35 A 67 44 A 78 44 3 # # # ## 9 ## 10 ## 11 ## 12 53 47 B 65 40 49 45 B 37 37 B 73 53 B 63 42 C 79 51 C 52 41 C 63 47 C 65 47 C 67 48 D 59 53 commUUUUUAAAA со мол во ме * # ## 16 # * # ## 19 ## 20 D 59 52 D 42 51 D 34 43 Step 1 : Running an ANOVA model on the data modell <- aov (y - Supplement + x, data= data df) summary (modell)

Step 1 : Running an ANOVA model on the data Supplement + x, data= data_df) modell <- aov (y summary (modell) Df Sum Sq Mean Sq F value Pr (>F) ## Supplement3 802 267.3 3.402 0.04545 * 1 1090 1090.2 13.874 0.00203 ** ## Residuals 15 1179 78.6 ++ --- ## Signif. codes: 0 ***** 0.001 "*** 0.01 "*0.05.' 0.1'ri Step 2: Running an ANCOVA model ##install.packages (car) Install the package if you do not have it. library (car) ## Loading required package: carData model2 <- Anova (modell, type="III") mode12 ## Anova Table (Type III tests) ## Response: y ## (Intercept) ## Supplement Sum Sq DE F value Pr (>F) 17.27 1 0.2198 0.645945 1501.05 3 6.3678 0.005352 ** 1090.18 1 13.8743 0.002033 ** 1178.62 15 ## X ## Residuals ## Signif. codes: 0 ****0.001 ***0.01 *0.05 .' 0.1' i The covariate, x, was significantly related to y, F(1,15) = 8.5092, p<0.01. The covariate Supplement also is significantly related to y, F(3,15) =6.3678. p<0.01